Chapter 6.5, Problem 3WE

To determine

To complete: the given statement by writing <, $=$ , Or >.

Answer to Problem 3WE

  $\begin{array}{l}XY>XZ\\ XW>12\end{array}$

Explanation of Solution

Given information:

Given figure,

  $\begin{array}{l}XY--XZ;\\ XW--12\end{array}$

Calculation:

Consider the following data:

  $\begin{array}{c}\angle XYW=48°\\ \angle YXW=40°\\ YW=12\\ WZ=12\end{array}$ .

In triangle $XYW$ ,

Since sum of three angles of a triangle is equal to $180°$

  $\begin{array}{c}\angle YWX=180°-\left(40°+48°\right)\\ =92°\end{array}$

Two angles $\angle YWX$ and $\angle XWZ$ forms linear pair,

Therefore,

  $\begin{array}{c}\angle XWZ=180°-92°\\ =88°\end{array}$

Since

$\overline{XW}$ is median of $\Delta XYZ$ therefore $\angle WXZ=40°$

  $\begin{array}{c}\angle WZX=180°-\left(40°+88°\right)\\ =52°\end{array}$

That is, $\angle ZYX<\angle YZX$

Therefore by Side-Angle-Side Inequality,

  $\begin{array}{l}XY>XZ\\ XW>12\end{array}$